I am blessed to say that I have three sons and five nephews. I have watched them all try and play different sports and been on the slopes with all of them. (The youngest is only 9 months as of today, so we will be patient with him.) They all ski except my youngest son, who snowboards. They are all pretty good and enjoy being on the hills.
They have also spent time on skateboards. Skateboarding and Skiing provide an interesting insight into the mind of young people. And a sobering lesson for adult coaches.
All of the boys have confidence in their bodies through success in other activities. To use current terms, they all have a high degree of physical literacy.
Between the seven of them, there were, maybe, two hours of formal, professional instruction for their snow sports. There was zero formal instruction for their skateboards.
My three sons could all "drop in" on their skateboards and they were not out-of-place at a skate park. They were making ramps, grinding rails, quarter-pipes, etc on our street. When I went outside to offer my two cents, their reaction was not exactly Christian-like.
They ditch us on the slopes on the first chance they get. The most popular places are the terrain parks because they know we won't go there and they are with their own kind, expressing themselves and free to fail. (I go to watch from a distance, and I am impressed every time)
WAIT! How did they learn how to ski and skateboard without a coach? How is that possible? Between YouTube, Tony Hawk on xBox and Blink 182 on their iPods, they had their coaching. A lot of band-aids and ice packs led to their comfort level. At the skate park they showed each other how to perform tricks, and happy to share. They imitated the pros as best they could and were not afraid to try again after failing (and falling). They have no issues with subsequent attempts being tried while bleeding or bruised.
The same went for the ski slopes. Snowboarding was a rebellious break away from the culture of skiing through age, styles, attitudes and approach. That culture has crept over to the young people skiing.
Ask kids why they like skateboarding and you can translate their answers to a few common thoughts ... fun, freedom and no adults. That's not entirely true. We pay for the decks, trucks, bearings and the "sick" wheels.
How did they learn without proper coaching?
We could flip that around and say they learn our team sports IN SPITE OF OUR INTERFERENCE.
Our children's imagination, courage and ability to learn should not be a surprise to us. We were like that. The only difference is our generation's parents allowed us to be like that.
If an athlete did take a deeper interest in something self-taught I would/could argue that they would need a coach to refine their technique to compete in a high-performance environment.
My suggestion to you is to take this mentality, embrace the built-in imagination and competence of our players and leave a part of training just for them and see what transpires.